O-LevelAdditional MathematicsStraight line graphs4037/22 · May/June 2016 · Q57 Marks
The coordinates of three points are A(−2, 6), B(6, 10) and C(p, 0).
- (i)Find the coordinates of M, the mid-point of AB.[2]
- (ii)Given that CM is perpendicular to AB, find the value of the constant p.[2]
- (iii)Find angle MCB.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.
- [B1, B1] (2, 8)
- [M1] (their8-0)/(their2-p) = -2 or better Condone (their8-0)/(their2-p) = -1/(their gradient AB) oe
- [A1] [p =] 6
- [M1] [MB =]√(6-their2)²+(10-their8)² soi or 1/2 [AB = √(6--2)² + (10-6)²] soi or [MC =]√(their2 - their p)² + (their8-0)² soi or tan[...] = 8/4 soi or 4.47² = 8.94² +10² – 2(8.94)(10) cos[...] or 8.94² = 10² +10² – 2(10)(10)cos[...] or sin⁻¹(√20/10) oe
- [M1] or cos⁻¹(√80/10) or tan⁻¹(√20/√80) or tan⁻¹(8/4) or 90 - tan⁻¹(8/4) or equivalent complete correct method; implies first M1
- [A1] 26.56 to 26.6° or 0.4636 to 0.464 rads cao Not from wrong working
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